Results 21 to 30 of about 60,649 (158)
International Journal of Engineering & Technology, 2018 A graph G with m vertices and n edges, is said to be prime graceful labeling, if there is an injection from the vertices of G to {1, 2, ..., k} where k = min {2m, 2n} such that gcd ( ( ), ( )=1 and the induced injective function from the edges of G to {1, 2, ..., k − 1} defined by ( ) = | ( ) − ( ) | , the resulting edge labels are distinct. In
R. Mohammad Abbas, T. Hameed Hassan
openaire +3 more sources
Graceful labeling of hexagonal snakes [PDF]
AIP Conference Proceedings, 2019 Consider a graph G with p number of vertices and q number of edges. If the edges of the graph are labeled by subtracting the corresponding vertex label of the respective edges following the condition that the labels of the vertices and edges are distinct is known as Graceful labeling of a graph.
Tamilselvi Loganathan +2 more
openaire +2 more sources
Graceful And Graceful Labeling Of Graphs
, 2018 {"references": ["1.\tJ. A. Gallian, A Dynamic survey of graph labeling, The electronic journal of combinatory 16 (2009).DS6. 2.\tI. Gutman, The energy of a graph, Ber. Math-satist. sekt. Forschungsz. Graz 103 (1978), 1-22. 3.\tGutman and B. Zhou, Laplacian energy of a graph, linear algebra appl. 414 (2006), 29-37. 4.\tI.
M. Soundharya, R. Balakumar
openaire +2 more sources
Graceful labeling on torch graph
Indonesian Journal of Combinatorics, 2018 Let G be a graph with vertex set V=V(G) and edge set E=E(G). An injective function f:V<span style="font-family: symbol;"> --> </span>{0,1,2,...,|E|} is called graceful labeling if f induces a function f<sup>*</sup>(uv)=|f(u)<span style="font-family: symbol;">-</span>f(v)| which is a bijection from E(G) to the ...
Jona Martinus Manulang, Kiki A. Sugeng
openaire +3 more sources
Graceful and Strongly Graceful Permutations [PDF]
arXiv, 2021 A graceful labelling of a graph G is an injective function f from the set of vertices of G into the set {0,1,...,|EG|} such that if edge uv is assigned the label |f(u)-f(v)| then all edge labels have distinct values. A strong graceful labelling of a tree T with a perfect matching is a graceful labelling of T with the additional property that the sum of
arxiv
EVEN GRACEFUL LABELLING OF A CLASS OF TREES
, 2019 A labelling or numbering of a graph G with q edges is an assignment of labels to the vertices of G that induces for each edge uv a labelling depending on the vertex labels f(u) and f(v). A labelling is called a graceful labelling if there exists an injective function f: V (G) → {0, 1,2,......q} such that for each edge xy, the labelling │f(x)-f(y)│is ...
T.K, Mathew Varkey, T.J, Rajesh Kumar
openaire +5 more sources
Graceful and Odd Graceful Labeling of Graphs
International Journal of Mathematics and Soft Computing, 2016 In this paper we prove gracefulness and odd gracefulness of arbitrary super -subdivision of triangular snake, where labeling of the vertices follows arithmetic progression.
openaire +2 more sources
Computer search for graceful labeling: a survey
Electronic Journal of Graph Theory and Applications, 2022 This paper surveys the main computer search results for finding graceful labeling of trees. The paper is devoted to the memory of Mirka Miller, who made an outstanding contribution to the area of graph labeling.
Ljiljana Brankovic, Michael J. Reynolds
openaire +2 more sources
Graceful and Prime Labelings -- Algorithms, Embeddings and Conjectures [PDF]
arXiv, 2020 Four algorithms giving rise to graceful graphs from a known (non)graceful graph are described. Some necessary conditions for a graph to be highly graceful and critical are given. Finally some conjectures are made on graceful, critical and highly graceful graphs. The RingelRosaKotzig Conjecture is generalized to highly graceful graphs.
arxiv
An Adiabatic Quantum Algorithm for Determining Gracefulness of A Graph [PDF]
, 2016 Graph labelling is one of the noticed contexts in combinatorics and graph theory. Graceful labelling for a graph $G$ with $e$ edges, is to label the vertices of $G$ with $0, 1, \cdots, e$ such that, if we specify to each edge the difference value between its two ends, then any of $1, 2, \cdots, e$ appears exactly once as an edge label.
arxiv +1 more source